Variational approximations using Fisher divergence

TL;DR

This paper introduces a new variational inference method based on Fisher divergence, offering a flexible and efficient alternative to traditional approaches, especially for complex models like logistic regression.

Contribution

It develops an efficient algorithm for Fisher divergence-based variational approximation that does not require conjugacy or mean-field assumptions, broadening applicability.

Findings

Outperforms traditional variational methods in logistic regression

Provides accurate posterior mean estimation

Handles complex models without conjugacy

Abstract

Modern applications of Bayesian inference involve models that are sufficiently complex that the corresponding posterior distributions are intractable and must be approximated. The most common approximation is based on Markov chain Monte Carlo, but these can be expensive when the data set is large and/or the model is complex, so more efficient variational approximations have recently received considerable attention. The traditional variational methods, that seek to minimize the Kullback--Leibler divergence between the posterior and a relatively simple parametric family, provide accurate and efficient estimation of the posterior mean, but often does not capture other moments, and have limitations in terms of the models to which they can be applied. Here we propose the construction of variational approximations based on minimizing the Fisher divergence, and develop an efficient computational algorithm that can be applied to a wide range of models without conjugacy or potentially unrealistic mean-field assumptions. We demonstrate the superior performance of the proposed method for the benchmark case of logistic regression.